Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Average Error: 20.5 → 5.7

Time: 53.6s

Precision: binary64

Cost: 16200

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \end{array} \]

Math

\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + \frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+57}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, \frac{x}{\frac{z}{\frac{y}{c}}}, t \cdot \frac{a \cdot -4}{c}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -4e-14)
     (+ (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* (/ (* t a) c) -4.0))
     (if (<= t_1 2e+57)
       (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)
       (if (<= t_1 1e+307)
         t_1
         (fma 9.0 (/ x (/ z (/ y c))) (* t (/ (* a -4.0) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -4e-14) {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) + (((t * a) / c) * -4.0);
	} else if (t_1 <= 2e+57) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	} else if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = fma(9.0, (x / (z / (y / c))), (t * ((a * -4.0) / c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-14)
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) + Float64(Float64(Float64(t * a) / c) * -4.0));
	elseif (t_1 <= 2e+57)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	elseif (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = fma(9.0, Float64(x / Float64(z / Float64(y / c))), Float64(t * Float64(Float64(a * -4.0) / c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-14], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+57], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], t$95$1, N[(9.0 * N[(x / N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	20.5
Target	14.4
Herbie	5.7

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -4e-14

   1. Initial program 14.6

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0 9.2

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   if -4e-14 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 2.0000000000000001e57

   1. Initial program 13.3

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 1.2

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      Proof
      (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 a (Rewrite<= metadata-eval (neg.f64 4))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 a) 4)) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite=> *-commutative_binary64 (*.f64 4 (neg.f64 a))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (*.f64 9 y)) b)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 9) y)) b) z)) c): 7 points increase in error, 2 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 b (*.f64 (*.f64 x 9) y))) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (*.f64 4 (neg.f64 a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 t 4) (neg.f64 a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 t)) (neg.f64 a)) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (*.f64 4 t) a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (neg.f64 (*.f64 (*.f64 4 t) a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> unsub-neg_binary64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (*.f64 4 t) a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite=> associate-*l*_binary64 (*.f64 4 (*.f64 t a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= metadata-eval (/.f64 4 1)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 4 (Rewrite<= *-inverses_binary64 (/.f64 z z))) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 4 z) z)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 4)) z) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 z 4) (/.f64 z (*.f64 t a))))) c): 15 points increase in error, 4 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 42 points increase in error, 12 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 17 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= associate-+r-_binary64 (+.f64 b (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)))) z) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b)) z) c): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))): 50 points increase in error, 51 points decrease in error

   if 2.0000000000000001e57 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.99999999999999986e306

   1. Initial program 0.6

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if 9.99999999999999986e306 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 63.7

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around 0 63.6

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   3. Simplified 21.1

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, a \cdot \left(t \cdot -4\right)\right)}{c}} \]
      Proof
      (/.f64 (fma.f64 9 (/.f64 y (/.f64 z x)) (*.f64 a (*.f64 t -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) z)) (*.f64 a (*.f64 t -4))) c): 25 points increase in error, 22 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 a t) -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (*.f64 (*.f64 a t) (Rewrite<= metadata-eval (neg.f64 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (*.f64 a t) 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 a t))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (neg.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (*.f64 4 (*.f64 a t)) 1)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (neg.f64 (/.f64 (*.f64 4 (*.f64 a t)) (Rewrite<= *-inverses_binary64 (/.f64 z z))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 4 (*.f64 a t)) z) z)))) c): 43 points increase in error, 4 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (neg.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 4 (*.f64 (*.f64 a t) z))) z))) c): 1 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (neg.f64 (/.f64 (*.f64 4 (Rewrite<= associate-*r*_binary64 (*.f64 a (*.f64 t z)))) z))) c): 21 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 9 (/.f64 (*.f64 y x) z)) (/.f64 (*.f64 4 (*.f64 a (*.f64 t z))) z))) c): 1 points increase in error, 1 points decrease in error
      (/.f64 (-.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 9 (*.f64 y x)) z)) (/.f64 (*.f64 4 (*.f64 a (*.f64 t z))) z)) c): 10 points increase in error, 12 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (*.f64 9 (*.f64 y x)) (*.f64 4 (*.f64 a (*.f64 t z)))) z)) c): 1 points increase in error, 1 points decrease in error
      (Rewrite=> associate-/l/_binary64 (/.f64 (-.f64 (*.f64 9 (*.f64 y x)) (*.f64 4 (*.f64 a (*.f64 t z)))) (*.f64 c z))): 39 points increase in error, 38 points decrease in error

   4. Taylor expanded in y around 0 33.1

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   5. Simplified 12.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{x}{\frac{z}{\frac{y}{c}}}, t \cdot \frac{-4 \cdot a}{c}\right)} \]
      Proof
      (fma.f64 9 (/.f64 x (/.f64 z (/.f64 y c))) (*.f64 t (/.f64 (*.f64 -4 a) c))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 x z) (/.f64 y c))) (*.f64 t (/.f64 (*.f64 -4 a) c))): 27 points increase in error, 25 points decrease in error
      (fma.f64 9 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 y c) (/.f64 x z))) (*.f64 t (/.f64 (*.f64 -4 a) c))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y x) (*.f64 c z))) (*.f64 t (/.f64 (*.f64 -4 a) c))): 34 points increase in error, 41 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 (*.f64 -4 a) c) t))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 -4 a) (/.f64 c t)))): 32 points increase in error, 32 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (Rewrite<= associate-*r/_binary64 (*.f64 -4 (/.f64 a (/.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (*.f64 -4 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a t) c)))): 25 points increase in error, 31 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z))) (*.f64 -4 (/.f64 (*.f64 a t) c)))): 1 points increase in error, 3 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -4 (/.f64 (*.f64 a t) c)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z))))): 0 points increase in error, 0 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 5.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + \frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{+57}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+307}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, \frac{x}{\frac{z}{\frac{y}{c}}}, t \cdot \frac{a \cdot -4}{c}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.6
Cost	11212

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-218}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + \frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(t_2 - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;\frac{b + \left(t_2 - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, \frac{x}{\frac{z}{\frac{y}{c}}}, t \cdot \frac{a \cdot -4}{c}\right)\\ \end{array} \]

Alternative 2
Error	7.4
Cost	11084

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-218}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + \frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(t_2 - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{b + \left(t_2 - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, a \cdot \left(t \cdot -4\right)\right)}{c}\\ \end{array} \]

Alternative 3
Error	9.3
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(t \cdot a\right) \cdot -4}{c}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 4
Error	9.3
Cost	6352

\[\begin{array}{l} t_1 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(t \cdot a\right) \cdot -4}{c}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 5
Error	7.3
Cost	6352

\[\begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := \frac{b + \left(t_1 - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ t_3 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(t \cdot a\right) \cdot -4}{c}\\ \mathbf{elif}\;t_3 \leq -4 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(t_1 - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)\right)}{c}\\ \mathbf{elif}\;t_3 \leq 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 6
Error	6.8
Cost	5324

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\right) + \frac{t \cdot a}{c} \cdot -4\\ t_3 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{-183}:\\ \;\;\;\;\frac{b + \left(t_3 - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;\frac{b + \left(t_3 - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	7.2
Cost	5324

\[\begin{array}{l} t_1 := \frac{t \cdot a}{c} \cdot -4\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{b}{z \cdot c}\\ t_4 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-218}:\\ \;\;\;\;\left(t_3 + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(t_4 - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)\right)}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+307}:\\ \;\;\;\;\frac{b + \left(t_4 - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t_3 + 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\right) + t_1\\ \end{array} \]

Alternative 8
Error	23.9
Cost	2024

\[\begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_3 := \frac{\frac{b}{z} + t_1}{c}\\ t_4 := \frac{t_1 + \frac{9}{\frac{z}{x \cdot y}}}{c}\\ \mathbf{if}\;a \leq -1.488891537910666 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.6657668983395242 \cdot 10^{-219}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;a \leq 2.0981911578768887 \cdot 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.7255055764383086 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 0.08713090063633963:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+235}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 9
Error	35.7
Cost	1504

\[\begin{array}{l} t_1 := \frac{x}{\frac{z \cdot \left(c \cdot 0.1111111111111111\right)}{y}}\\ \mathbf{if}\;t \leq -27.442274566119046:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq -1.3133133693695052 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.0374337472918403 \cdot 10^{-59}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;t \leq -1.0072142578259916 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -2.5300358396789478 \cdot 10^{-261}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;t \leq -6.530649510721274 \cdot 10^{-282}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 6.1435204897948565 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4599752541762062 \cdot 10^{-45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 10
Error	27.6
Cost	1496

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.0857194121841613 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq -1.3133133693695052 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.0374337472918403 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.868925330522605 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 11
Error	36.5
Cost	1372

\[\begin{array}{l} t_1 := \frac{x}{\frac{z \cdot \left(c \cdot 0.1111111111111111\right)}{y}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;z \leq -3.743569258274533 \cdot 10^{+65}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-40}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.001635744132254 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t \cdot a\right) \cdot -4}{c}\\ \end{array} \]

Alternative 12
Error	36.6
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.584571168057116 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.592399329789 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	36.6
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{\left(t \cdot a\right) \cdot -4}{c}\\ t_3 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.584571168057116 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.592399329789 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	34.8
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := t \cdot \frac{a \cdot -4}{c}\\ t_3 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.584571168057116 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.592399329789 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	34.7
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := t \cdot \frac{a \cdot -4}{c}\\ t_3 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.584571168057116 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.592399329789 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	34.5
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_3 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.584571168057116 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.592399329789 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	34.3
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.584571168057116 \cdot 10^{-127}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.905415581369754 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.592399329789 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 18
Error	18.9
Cost	1232

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{\frac{b}{z} + \left(t \cdot a\right) \cdot -4}{c}\\ \mathbf{if}\;z \leq -9.44613614897936 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6730354399897746 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	18.9
Cost	1232

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{\frac{b}{z} + \left(t \cdot a\right) \cdot -4}{c}\\ \mathbf{if}\;z \leq -9.44613614897936 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.6730354399897746 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	18.8
Cost	1232

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + \left(t \cdot a\right) \cdot -4}{c}\\ \mathbf{if}\;z \leq -9.44613614897936 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.6730354399897746 \cdot 10^{+22}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	42.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 22
Error	43.2
Cost	320

\[\frac{\frac{b}{c}}{z} \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))